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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.1.d.a 128.d 8.d $1$ $0.064$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\)
128.2.a.a 128.a 1.a $1$ $1.022$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.b 128.a 1.a $1$ $1.022$ \(\Q\) None None \(0\) \(-2\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.c 128.a 1.a $1$ $1.022$ \(\Q\) None None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
128.2.a.d 128.a 1.a $1$ $1.022$ \(\Q\) None None \(0\) \(2\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
128.2.b.a 128.b 8.b $2$ $1.022$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}-5q^{9}+\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots\)
128.2.b.b 128.b 8.b $2$ $1.022$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+3q^{9}-iq^{13}-2q^{17}-11q^{25}+\cdots\)
128.2.e.a 128.e 16.e $2$ $1.022$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(1+i)q^{5}+2iq^{7}+\cdots\)
128.2.e.b 128.e 16.e $2$ $1.022$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(1+i)q^{5}-2iq^{7}+iq^{9}+\cdots\)
128.2.g.a 128.g 32.g $4$ $1.022$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
128.2.g.b 128.g 32.g $8$ $1.022$ 8.0.18939904.2 None None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
128.2.k.a 128.k 128.k $240$ $1.022$ None None \(-16\) \(-16\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{32}]$
128.3.c.a 128.c 4.b $4$ $3.488$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}+(-2-\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots\)
128.3.c.b 128.c 4.b $4$ $3.488$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}+(2+\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
128.3.d.a 128.d 8.d $2$ $3.488$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}-9q^{9}+3iq^{13}+30q^{17}+\cdots\)
128.3.d.b 128.d 8.d $2$ $3.488$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+23q^{9}-3\beta q^{11}-2q^{17}+\cdots\)
128.3.d.c 128.d 8.d $4$ $3.488$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
128.3.f.a 128.f 16.f $6$ $3.488$ 6.0.399424.1 None None \(0\) \(-2\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
128.3.f.b 128.f 16.f $6$ $3.488$ 6.0.399424.1 None None \(0\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
128.3.h.a 128.h 32.h $28$ $3.488$ None None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$
128.3.l.a 128.l 128.l $496$ $3.488$ None None \(-16\) \(-16\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{32}]$
128.4.a.a 128.a 1.a $1$ $7.552$ \(\Q\) None None \(0\) \(-2\) \(-6\) \(20\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-6q^{5}+20q^{7}-23q^{9}-14q^{11}+\cdots\)
128.4.a.b 128.a 1.a $1$ $7.552$ \(\Q\) None None \(0\) \(-2\) \(6\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+6q^{5}-20q^{7}-23q^{9}-14q^{11}+\cdots\)
128.4.a.c 128.a 1.a $1$ $7.552$ \(\Q\) None None \(0\) \(2\) \(-6\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-6q^{5}-20q^{7}-23q^{9}+14q^{11}+\cdots\)
128.4.a.d 128.a 1.a $1$ $7.552$ \(\Q\) None None \(0\) \(2\) \(6\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+6q^{5}+20q^{7}-23q^{9}+14q^{11}+\cdots\)
128.4.a.e 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None None \(0\) \(-4\) \(-4\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+(-2-2\beta )q^{5}+(-4+\cdots)q^{7}+\cdots\)
128.4.a.f 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None None \(0\) \(-4\) \(4\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+(2+2\beta )q^{5}+(4+2\beta )q^{7}+\cdots\)
128.4.a.g 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None None \(0\) \(4\) \(-4\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(-2+2\beta )q^{5}+(4-2\beta )q^{7}+\cdots\)
128.4.a.h 128.a 1.a $2$ $7.552$ \(\Q(\sqrt{3}) \) None None \(0\) \(4\) \(4\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(2-2\beta )q^{5}+(-4+2\beta )q^{7}+\cdots\)
128.4.b.a 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-64\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-3iq^{5}-2^{5}q^{7}-37q^{9}+\cdots\)
128.4.b.b 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+19q^{9}+5^{2}\beta q^{11}-90q^{17}+\cdots\)
128.4.b.c 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+3^{3}q^{9}+23iq^{13}+94q^{17}+\cdots\)
128.4.b.d 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(64\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+3iq^{5}+2^{5}q^{7}-37q^{9}+\cdots\)
128.4.b.e 128.b 8.b $4$ $7.552$ \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-13q^{9}+\cdots\)
128.4.e.a 128.e 16.e $10$ $7.552$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}-\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots\)
128.4.e.b 128.e 16.e $10$ $7.552$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{3}-\beta _{3}q^{5}+(-3\beta _{1}+\beta _{4})q^{7}+\cdots\)
128.4.g.a 128.g 32.g $44$ $7.552$ None None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$
128.4.k.a 128.k 128.k $752$ $7.552$ None None \(-16\) \(-16\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{32}]$
128.5.c.a 128.c 4.b $8$ $13.231$ 8.0.205520896.4 None None \(0\) \(0\) \(-48\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-6-\beta _{2})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
128.5.c.b 128.c 4.b $8$ $13.231$ 8.0.205520896.4 None None \(0\) \(0\) \(48\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(6+\beta _{2})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)
128.5.d.a 128.d 8.d $2$ $13.231$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-iq^{5}-3^{4}q^{9}+5iq^{13}-322q^{17}+\cdots\)
128.5.d.b 128.d 8.d $2$ $13.231$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+47q^{9}+21\beta q^{11}+574q^{17}+\cdots\)
128.5.d.c 128.d 8.d $4$ $13.231$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+15q^{9}+\cdots\)
128.5.d.d 128.d 8.d $8$ $13.231$ 8.0.1871773696.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(55-\beta _{6}+\cdots)q^{9}+\cdots\)
128.5.f.a 128.f 16.f $14$ $13.231$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-2\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(-19\beta _{1}+\cdots)q^{9}+\cdots\)
128.5.f.b 128.f 16.f $14$ $13.231$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{9}q^{7}+(19\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
128.5.h.a 128.h 32.h $60$ $13.231$ None None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$
128.5.l.a 128.l 128.l $1008$ $13.231$ None None \(-16\) \(-16\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{32}]$
128.6.a.a 128.a 1.a $1$ $20.529$ \(\Q\) None None \(0\) \(-6\) \(-94\) \(-244\) $-$ $\mathrm{SU}(2)$ \(q-6q^{3}-94q^{5}-244q^{7}-207q^{9}+\cdots\)
128.6.a.b 128.a 1.a $1$ $20.529$ \(\Q\) None None \(0\) \(-6\) \(94\) \(244\) $-$ $\mathrm{SU}(2)$ \(q-6q^{3}+94q^{5}+244q^{7}-207q^{9}+\cdots\)
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